The equivalent circuit is wrong in several regards. The inductance is a series rather than a parallel element. There will be an inductive coupling of both wires.
As a first order estimation, I would use three ideal transmission lines, two single ended modelling the wires above a groundplanes and a differential representing the coupling. It's parameters can be derived from extracted partial L and C elements.
A 2-D electrostatic respectively AC magnetic simulation can be used to extract the L and C elements. I would assume both ground planes shorted for simplification. otherwise a fourth differential TL has to be used in the simulation.
Of course a true 3D EM solver can handle the problem, but the thin wire involves a large meshing effort.